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人気のある微分積分 >

簡約 ln(sqrt((a^2-z^2)/(a^2+z^2)))

解

簡約

ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

解

\frac{1}{2} ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

解答ステップ

ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

書き換え

= ln ((\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})^{\frac{1}{2}})

以下のように仮定して対数の規則

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

を適用する:

x \geq 0

= \frac{1}{2} ln (\frac{- z ^{2} + a ^{2}}{z ^{2} + a ^{2}})

人気の例

limit as x approaches 5 of (x-5)/(x-5)

x \to 5 lim (\frac{x - 5}{x - 5})

limit as x approaches 1 of 18x^{100}-5

x \to 1 lim (18 x^{100} - 5)

integral from 1 to 3 of (3x^2+4)

\int_{1}^{3} (3 x^{2} + 4) d x

(dy)/(dx)=(-0.1)/(cos(y)),y(0)= pi/2

\frac{d y}{d x} = \frac{- 0.1}{cos ( y )}, y (0) = \frac{π}{2}

sum from n=0 to infinity of n*2^{n-1}

n = 0 \sum \infty n \cdot 2^{n - 1}